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Add original (Chambolle) implementation of TV denoising

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Johannes Schönberger
2012-12-25 11:15:41 +01:00
parent ae5488a2b1
commit 236ef48ec9
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skimage/filter/__init__.py
+1
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@@ -3,6 +3,7 @@ from .ctmf import median_filter
from ._canny import canny
from .edges import (sobel, hsobel, vsobel, scharr, hscharr, vscharr, prewitt,
hprewitt, vprewitt)
from ._denoise import denoise_tv_chambolle, tv_denoise
from ._denoise_cy import denoise_bilateral, denoise_tv_bregman
from ._rank_order import rank_order
from .thresholding import threshold_otsu, threshold_adaptive
skimage/filter/_denoise.py
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@@ -0,0 +1,261 @@
import numpy as np
from skimage import img_as_float
from skimage._shared.utils import deprecated
def _denoise_tv_chambolle_3d(im, weight=100, eps=2.e-4, n_iter_max=200):
"""Perform total-variation denoising on 3D images.
Parameters
----------
im : ndarray
3-D input data to be denoised.
weight : float, optional
Denoising weight. The greater `weight`, the more denoising (at
the expense of fidelity to `input`).
eps : float, optional
Relative difference of the value of the cost function that determines
the stop criterion. The algorithm stops when:
(E_(n-1) - E_n) < eps * E_0
n_iter_max : int, optional
Maximal number of iterations used for the optimization.
Returns
-------
out : ndarray
Denoised array of floats.
Notes
-----
Rudin, Osher and Fatemi algorithm.
Examples
---------
>>> x, y, z = np.ogrid[0:40, 0:40, 0:40]
>>> mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2
>>> mask = mask.astype(np.float)
>>> mask += 0.2 * np.random.randn(*mask.shape)
>>> res = denoise_tv(mask, weight=100)
"""
px = np.zeros_like(im)
py = np.zeros_like(im)
pz = np.zeros_like(im)
gx = np.zeros_like(im)
gy = np.zeros_like(im)
gz = np.zeros_like(im)
d = np.zeros_like(im)
i = 0
while i < n_iter_max:
d = - px - py - pz
d[1:] += px[:-1]
d[:, 1:] += py[:, :-1]
d[:, :, 1:] += pz[:, :, :-1]
out = im + d
E = (d**2).sum()
gx[:-1] = np.diff(out, axis=0)
gy[:, :-1] = np.diff(out, axis=1)
gz[:, :, :-1] = np.diff(out, axis=2)
norm = np.sqrt(gx**2 + gy**2 + gz**2)
E += weight * norm.sum()
norm *= 0.5 / weight
norm += 1.
px -= 1. / 6. * gx
px /= norm
py -= 1. / 6. * gy
py /= norm
pz -= 1 / 6. * gz
pz /= norm
E /= float(im.size)
if i == 0:
E_init = E
E_previous = E
else:
if np.abs(E_previous - E) < eps * E_init:
break
else:
E_previous = E
i += 1
return out
def _denoise_tv_chambolle_2d(im, weight=50, eps=2.e-4, n_iter_max=200):
"""Perform total-variation denoising on 2D images.
Parameters
----------
im : ndarray
Input data to be denoised.
weight : float, optional
Denoising weight. The greater `weight`, the more denoising (at
the expense of fidelity to `input`)
eps : float, optional
Relative difference of the value of the cost function that determines
the stop criterion. The algorithm stops when:
(E_(n-1) - E_n) < eps * E_0
n_iter_max : int, optional
Maximal number of iterations used for the optimization.
Returns
-------
out : ndarray
Denoised array of floats.
Notes
-----
The principle of total variation denoising is explained in
http://en.wikipedia.org/wiki/Total_variation_denoising.
This code is an implementation of the algorithm of Rudin, Fatemi and Osher
that was proposed by Chambolle in [1]_.
References
----------
.. [1] A. Chambolle, An algorithm for total variation minimization and
applications, Journal of Mathematical Imaging and Vision,
Springer, 2004, 20, 89-97.
Examples
---------
>>> from skimage import color, data
>>> lena = color.rgb2gray(data.lena())
>>> lena += 0.5 * lena.std() * np.random.randn(*lena.shape)
>>> denoised_lena = denoise_tv(lena, weight=60)
"""
px = np.zeros_like(im)
py = np.zeros_like(im)
gx = np.zeros_like(im)
gy = np.zeros_like(im)
d = np.zeros_like(im)
i = 0
while i < n_iter_max:
d = -px - py
d[1:] += px[:-1]
d[:, 1:] += py[:, :-1]
out = im + d
E = (d**2).sum()
gx[:-1] = np.diff(out, axis=0)
gy[:, :-1] = np.diff(out, axis=1)
norm = np.sqrt(gx**2 + gy**2)
E += weight * norm.sum()
norm *= 0.5 / weight
norm += 1
px -= 0.25 * gx
px /= norm
py -= 0.25 * gy
py /= norm
E /= float(im.size)
if i == 0:
E_init = E
E_previous = E
else:
if np.abs(E_previous - E) < eps * E_init:
break
else:
E_previous = E
i += 1
return out
def denoise_tv_chambolle(im, weight=50, eps=2.e-4, n_iter_max=200,
multichannel=False):
"""Perform total-variation denoising on 2D and 3D images.
Parameters
----------
im : ndarray (2d or 3d) of ints, uints or floats
Input data to be denoised. `im` can be of any numeric type,
but it is cast into an ndarray of floats for the computation
of the denoised image.
weight : float, optional
Denoising weight. The greater `weight`, the more denoising (at
the expense of fidelity to `input`).
eps : float, optional
Relative difference of the value of the cost function that
determines the stop criterion. The algorithm stops when:
(E_(n-1) - E_n) < eps * E_0
n_iter_max : int, optional
Maximal number of iterations used for the optimization.
multichannel : bool, optional
Apply total-variation denoising separately for each channel. This
option should be true for color images, otherwise the denoising is
also applied in the 3rd dimension.
Returns
-------
out : ndarray
Denoised image.
Notes
-----
The principle of total variation denoising is explained in
http://en.wikipedia.org/wiki/Total_variation_denoising
The principle of total variation denoising is to minimize the
total variation of the image, which can be roughly described as
the integral of the norm of the image gradient. Total variation
denoising tends to produce "cartoon-like" images, that is,
piecewise-constant images.
This code is an implementation of the algorithm of Rudin, Fatemi and Osher
that was proposed by Chambolle in [1]_.
References
----------
.. [1] A. Chambolle, An algorithm for total variation minimization and
applications, Journal of Mathematical Imaging and Vision,
Springer, 2004, 20, 89-97.
Examples
---------
2D example on Lena image:
>>> from skimage import color, data
>>> lena = color.rgb2gray(data.lena())
>>> lena += 0.5 * lena.std() * np.random.randn(*lena.shape)
>>> denoised_lena = denoise_tv(lena, weight=60)
3D example on synthetic data:
>>> x, y, z = np.ogrid[0:40, 0:40, 0:40]
>>> mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2
>>> mask = mask.astype(np.float)
>>> mask += 0.2*np.random.randn(*mask.shape)
>>> res = denoise_tv(mask, weight=100)
"""
im_type = im.dtype
if not im_type.kind == 'f':
im = img_as_float(im)
if im.ndim == 2:
out = _denoise_tv_2d(im, weight, eps, n_iter_max)
elif im.ndim == 3:
if multichannel:
out = np.zeros_like(im)
for c in range(im.shape[2]):
out[..., c] = _denoise_tv_2d(im[..., c], weight, eps,
n_iter_max)
else:
out = _denoise_tv_3d(im, weight, eps, n_iter_max)
else:
raise ValueError('only 2-d and 3-d images may be denoised with this '
'function')
return out
tv_denoise = deprecated('skimage.filter.denoise_tv_chambolle')\
(denoise_tv_chambolle)